Four terminal equaliser networks



Jan. 21, 1958 J. J. A. GRABAU ETAL 2,820,950

FOUR TERMINAL EQUALISER NETWORKS Filed Sept. 30, 1954 2 Sheets-Sheet 1' 1 4 Z N V R R x: db 0 Inventors JOAC/l/M .JUSTl/S ANDREAS GRABAU.

5 WOLJA SARAGA J. J. A. GRABAU ETAL 2,820,950

FOUR TERMINAL EQUALISER NETWORKS Jan. 21, 1958 Filed Sept. 30. 1954 2 Sheets-Sheet 2 m B 1 4 O Inventors JOACH/M JUSTUS ANDREAS GEABAU 8 WOLJA SAIPAGA Attorneys FOUR TERMINAL EQUALISER NETWORKS.

Joachim Justus Andreas Grabau, Liverpool, and Wolja Saraga, Orpington, England, assignors to Automatic Telephone & Electrical Company Limited, Liverpool,

' England, a British company Application September 30, 1954, Serial No. 459,306

Claims priority, application Great Britain October 22, 1953 Claims. (Cl. 333-28) The present invention relates tofour-terminal equaliser networks whose driving point impedance varies with frequency. More particularly the invention is concerned with four-terminal networks consisting of lumped resistors, capacitors and inductors, and whose primary driving point impedance varies in a stipulated manner both with frequency and with the impedance connected to the secondary terminals.

A special application for networks-of this general type is the variable slope equaliser frequently employed in carrier transmission system equipped with automatic gain control. istics of an open-wire line are equalised in two stages, the functions of the two parts of the gain control equipment being respectively to provide for an adjustment of gain which istequalatrall frequencies-in-the transmitted band, and to provide; for an adjustmentofgain which is a linear function of frequency within the transmission band. The characteristics of a network designed in accordance with this latter requirement must also include a hinge frequency which may be Within, outside, or at one end of the transmitted band, i. e. a frequency at-which'themodulusof thedriving point impedance remains constant when the slope of the gain/ frequency characteristic is varied.

It is the object of the invention to provide a simple network of which thelogarithmof the modulus of its driving point impedance is a substantially linear function-of frequency ina limited frequency interval, the functio'nbeing variable with change of theterminating impedance, while at a given frequency within the interval the modulus is constant and does not vary with change of terminating impedance.

According to another feature of the invention, in a symmetrical four-terminal network having an image impedance which is constant and real for all frequencies within a limited frequency range and which when terminated by a resistor has a driving point impedance the logarithm of Whose modulus varieswith frequency; over said limited frequency range as a substantially linear function the slope of which varies with the value of the terminating resistor, the components. are so..selected.as to make the image phase shift equal .to one of the values 45 deg.:n90 deg, n being. a positive integer .at that.frequency within said range of frequencies at which the driving point impedance is desired to be maintained constant and independent of the terminating resistor.

The nature of the invention will be understood from the following description, which-should. ,berreadinzcom junction with the accompanying drawingscomprisingFigs. 1-9. v

' Of these,

Fig.1 shows the arrangement ofthe network of .the in-- vention and its connection to its terminating impedance,';

Fig. 2 shows the modulus of the driving point impedance of the network of theinvention drawn as a function of the phase-shift and of the terminating impedance,

Fig. 3 shows the: generalv form of a constant resistance balanced lattice network,

In such a system, the transmission character- United States Patent Ofiice 2,820,950 Patented: Jane 21, 1 958 Figs. 4 and 5 show networks which are equivalent-under certain conditions to that shown in Fig. 3,

Figs. 6 and 7 show networks. derived from that of Fig. 5 after assigning special values to its elements,

Fig. 8 shows theperformance diagram of a particular network illustrating the invention and Fig. 9 shows the component values of thisnetwork.

A linear relation between the logarithm of the driving point impedance of thetnetworkand frequency can be expressed as:

Z denotes the modulus :of the "primary driving point impedance |Z| of the network, which can be considered as being terminated by a purely resistive impedance R f is frequency;

i is. the hinge frequency at whichZ is to be constant,

b is a factor depending on and varying with the terminating resistance R,;,

and

a isa constant.

While no physical network exists whose driving-point impedance varies accurately in accordance withthe above equation, .it. can. betshown 4 that good approximations can beobtainedffor limitedfrequency intervals, The .generalarrangement of the network N in relationtoits terminatingresistor is shown in Fig. 1,- fromwhich it will be seen thatits driving-point-impedance is measured-atterminals 1 and 2, while the terminating resistor R is connected to terminals 13 and 4.

In the following. description it is; assumed that the fundamental principles of four-terminal network analysis are understood, and reference should, where necessary, be made'to the-standard textbooks dealing with this subject, e. g. ElectricalCircuitsand Wave Filters by AFT. Starr: Sir Isaac Pitman & SonsLtd., 1940.

The driving-point. impedance Z of a symmetricalzfourterminalnetwork, having an image impedance 2;, an image transfer constant where :A is. the image attenuation and Bistheimage phase shift, and terminated by a resistance R -may-be written :as:

R Z- r-l-tanh 0. R R,

1+ tanh 6 and with the modulus:

provided A=0, and in the general case where A O,

shift variable B in Fig. 2 may be regarded as a distorted frequency scale. In any particular network the relation between B and 1 will be fixed and with a suitable choice of network it will frequently be possible to establish the required linear relation between Ill and I, especially if the network exhibits phase shift values which are different from B=, -90, i180" and so on, in the frequency range of interest.

By including suitable resistive elements in the network, thereby making A 0, it is possible to select ranges for which the general character of the oc/fl curves is not: much different from that shown in Fig. 2. The additional parameters made available in this way can be used to assist in linearising the characteristics.

Numerous networks can be found for which the relation between a: and B is of such a nature as to permit the realisation of linear characteristics for a0) according to the invention. Of special interest, however, are symmetrical networks having an image impedance R which is constant and real for all frequencies. These networks can be realised as balanced lattices of the type shown in Fig. 3. These have series and diagonal arms, the product of whose impedances Z,, and Z, is equal'to the square of R. Equivalent to this lattice is the balanced or un-' balanced bridged-T circuit, of which the unbalanced type is shown in Fig. 4. It will be obvious that this circuit' One of the networks obtained in this way is shown in Fig. 5. If it turns out that 2,, permits representation as a series combination of an inductance:

. kL- 2 (where p= l .21rf) and a capacitance: A

such that k is not negative but is less than one, then the star-combination of Z in Fig. 5, can be replaced by a transformer coil as shown in Fig. 6.

A further simplification arises in the case where k=0, when the circuit is reduced to a coupled coil without leakage flux and one capacitor, as shown in Fig. 7.

The relation between the image transfer constant 95 and the impedance Z of the diagonal arm of the balanced lattice network is given by the equation:

which reduces for a purely reactive impedance Z to:

Z -1 B 2 cot JR 7 In the general case 2,, can be expressed as:

with r and s real, and r50.

The condition for the presence of a hingefrequency i may be stated as follows:

The sufiix h indicates that the values are taken at the frequency f=f;,.

In order for this last expression to lead to a real value for s,,, the condition must be satisfied. If, furthermore, the network should be capable of being transformed into the bridged-T type shown in Fig. 5, the restriction of r assumes the form;

Rgr gvizz Frequently the network is part of a circuit whose un-' avoidable stray capacitances add an undesirable capacitive shunt to one or both pairs of the terminals, and the result may be the disappearance of a sharply defined hinge frequency. In this case it will generally be .possible to neutralise the capacitive eifect by connecting a suitable inductor across the terminals which, at the hinge frequency, resonates with the stray capacitance measured at that point. H r

The design of a specific network will now be described by way of example, the resulting network being of the kind shown in Fig. 7. The problem for consideration is the provision of a network whose characteristics in the frequency interval 3684 kc./s. The hinge frequency is required to be kc./s., and at 36 kc./s. the

quantity or should vary monotonously from 6 db to +6 db while increases from {0.2 to 5.

A glance at Fig. 2 shows that under the stated condi-.

tions the phase shift B at the frequency f;, couldbe, amongst other values, 45. Assuming the network to be purely reactive it will be seen from the foregoing that,

at the hinge frequency:

It can be shown that the phase-shift at 36 kc./ s. should vary from 24.5 downwards, the optimum value being obtained by trial and error so as to produce the best linearity of the characteristics. It happens in this particular example that the optimum condition is very close to that which allows the realisation of the network shown in Fig. 7. The equation for this network, derived from those set out in connection with Figs. 5 and 6, can be written:

The phase shift B at 36 kc./ s. is then:

B 80 1 [f 36 Ink/5'] 2 cot 36 2.414

which is in fact, lower than 24.5".

After obtaining the value of C from the relation:

the characteristics (f) may be obtained from the equation for Fig. 2 after calculating B from:

=2 tan" (2 11;! RC) The diagram of (1(1) with as a parameter is shown in Fig. 8 with L=R C and R=l500i2 the elemental values of the network are as shown in Fig. 9.

We claim:

1. A four-terminal network having an image impedance which is constant and real for all frequencies within a limited frequency range and which when terminated by a resistor has a driving point impedance the logarithm of whose modulus varies with frequency over said limited range as a substantially linear function, the slope of which varies with the value of the terminating resistor, the network being formed of components which make the image phase shift equal to one of the values 45 deg. in 90 deg., n being a positive integer, at a frequency within said limited frequency range at which the driving point impedance is desired to be maintained constant and independent of the terminating resistor.

2. A four-terminal symmetrical network as claimed in claim 1 and comprising a balanced lattice network having series and diagonal impedances whose product equals the square of the image impedance, the series and diagonal impedances being two terminal networks.

3. A four-terminal network as claimed in claim 1 and comprising series and shunt arms, a two winding inductive coil having total impedance L, the first winding being connected in the series arm and having impedance 2L while the second winding is connected in the shunt arm and has impedance an impedance 2L while the other winding is connected in the shunt arm and has an impedance and a capacitor in series with said second winding and having an impedance where R is the image impedance of the network.

5. A four-terminal network as claimed in claim 1 and comprising an inductor connected across at least one pair of terminals of the network to compensate the inherent capacity effects, the inductor resonating with said inherent capacity at the frequency at which the driving point impedance is desired to be maintained constant and independent of the terminating resistance.

References Cited in the file of this patent UNITED STATES PATENTS 1,970,933 Frederick Aug. 21, 1934 1,991,195 Darlington Feb. 12, 1935 2,035,258 Bode Mar. 24, 1936 2,694,184 Rounds Nov 9. 1954 2,698,420 Saraga Dec. 28, 1954 2,758,281 Carleson Aug. 7, 1956 UNITED STATES PATENT OFFICE CERTIFICATE 9F CORRECTION Patent N00 2,820,950 January 21, 1958 Joachim Justus Andreas Grabau et a1 requiring correction and that the said Letters Patent should read as cor= rect'ed' below In the "grant, lines 2' and 3, and line 13, and in the heading to the printed specification, lines 4 and 5, name of as'sign'ee, for "Automatic Telephone & Electrical Company Limited" read Automatic Telephone 8: Electric Company Limited Signed and sealed this 22nd day of April 1958a (SEAL) Attest: r- KARL MINE ROBERT C. WATSON Attesting Officer Commissioner of Patents 

